Sturridge has not featured for Liverpool since sustaining a thigh injury during a training session in the previous international break at the beginning of September.
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Rodgers got his wish after England boss Hodgson chose not to name the 25-year-old striker in his 21-man squad for the Euro 2016 qualifying double-header with San Marino and Estonia later this month.
However, Hodgson insists the decision was based on Sturridge's fitness, rather than any kind of rift with Liverpool.
Asked if he was outmanoeuvred, Hodgson replied: "No, there's been no question of manoeuvring on our part or Liverpool's part.
"It's just simply a fact, an unfortunate fact, that he's not recovered. It's a great blow to us, Liverpool and the player, because he was anxious to be a part of these two games. There's no problems or conflict there at all.
"He's not played for Liverpool at all since picking up the injury with us. As I understand it he's still got some work to do before he's fully fit. There was no question of him being selected."
Hodgson also defended his management of Sturridge after Rodgers claimed that the injury was a result of England not following Liverpool's training schedule.
"We always try to do that. The last thing you want is to get injuries in training, even more so as an international manager because you feel a responsibility to the clubs," he added.
"People need to consider that we have such a shortage of time. On this particular occasion we had two days and two training sessions to try and hone a very different way of playing.
"If I'm going to be put under pressure as the England manager in future to give every player two days off every time they play, then we won't train at all quite frankly."